On the excessive<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>[</mml:mo><mml:mi>m</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:math>-index of a tree

Mazzuoccolo, Giuseppe

doi:10.1016/j.dam.2013.08.014

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…For

B > 3

a general formula for

χ^{'} [B] (G)

is presently unknown. Only for trees, a most basic and simple class of graphs, such a formula has been recently obtained for

B = 4

. However, it has been proved in that the problem of the computation of

χ^{'} [B] (G)

can be solved in polynomial time for the class of bipartite multigraphs.…”

Section: Notation Terminology and Auxiliary Resultsmentioning

confidence: 99%

On the Complexity of Computing the Excessive [B]‐Index of a Graph

Cariolaro

Rizzi

2015

Journal of Graph Theory

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Let B be a positive integer and let G be a simple graph. An excessive [B]‐factorization of G is a minimum set of matchings, each of size B, whose union is E(G). The number of matchings in an excessive [B]‐factorization of G (or ∞ if an excessive [B]‐factorization does not exist) is a graph parameter called the excessive [B]‐index of G and denoted by χ[B]′(G). In this article we prove that, for any fixed value of B, the parameter χ[B]′(G) can be computed in polynomial time in the size of the graph G. This solves a problem posed by one of the authors at the 21st British Combinatorial Conference.

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“…For

B > 3

a general formula for

χ^{'} [B] (G)

is presently unknown. Only for trees, a most basic and simple class of graphs, such a formula has been recently obtained for

B = 4

. However, it has been proved in that the problem of the computation of

χ^{'} [B] (G)

can be solved in polynomial time for the class of bipartite multigraphs.…”

Section: Notation Terminology and Auxiliary Resultsmentioning

confidence: 99%

On the Complexity of Computing the Excessive [B]‐Index of a Graph

Cariolaro

Rizzi

2015

Journal of Graph Theory

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“…[1,2,4,5,7,12,13,15]) and connections with some important combinatorial problems such as the Berge-Fulkerson Conjecture have already been noticed [11].…”

Section: Introductionmentioning

confidence: 92%

Excessive[l,m]-factorizations

Cariolaro

Mazzuoccolo

2015

Discrete Mathematics

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MatchingChromatic index a b s t r a c t Given two positive integers l and m, with l ≤ m, an [l, m]-covering of a graph G is a set M of matchings of G whose union is the edge set of G and such that l ≤ |M| ≤ m for everythe cardinality of M is as small as possible. The number of matchings in an excessive [l, m]-factorization of G (or ∞, if G does not admit an excessive [l, m]-factorization) is a graph parameter called the excessive [l, m]-index of G and denoted by χ ′ [l,m] (G). In this paper we study such parameter. Our main result is a general formula for the excessive [l, m]-index of a graph G in terms of other graph parameters. Furthermore, we give a polynomial time algorithm which computes χ ′ [l,m] (G) for any fixed constants l and m and outputs an excessive [l, m]-factorization of G, whenever the latter exists.

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